Question

For reasonable distances, a certain jogger can maintain an average speed of 6 miles per hour while running on level ground. The jogger decides to go to a local park and use one of the paths there for a workout routine one day each week. This path is a gently sloping one that winds its way to the top of a hill.

1. The jogger can run at an average speed of 5.5 miles per hour up the slope and 6.5 miles per hour going down the slope. The jogger decides to cover 2 miles by going uphill for 1 mile and then returning 1 mile back down the hill.

a. How long does it take the jogger to run 1 mile uphill? __ (Hint: Use the formula d = rt.)

b. How long does it take the jogger to run 1 mile downhill? _____ (Hint: Use the formula d = rt.)

c. Use your answers to a and b to determine how long, in hours, the full trip will take (1 mile uphill and 1 mile downhill). Give an exact answer expressed as a fraction in simplest terms and then give a decimal approximation correct to three decimal places. Reduced Fraction: _________ Decimal Approximation: _________

Answer 1

Part a) How long does it take the jogger to run 1 mile uphill?

we know that
speed=distance/time
speed=5.5 miles/hour-----> r
distance=1 mile------> d
time=?-----> t
d=r*t------> t=d/r
t=1 mile/5.5 mile/hour-------> t=0.182 hour----> t=2/11 hour

the answer Part a) is
0.182 hour

Part b)How long does it take the jogger to run 1 mile downhill?
we know that
speed=distance/time
speed=6.5 miles/hour-----> r
distance=1 mile------> d
time=?-----> t
d=r*t------> t=d/r
t=1 mile/6.5 mile/hour-------> t=0.154 hour-----> t=2/13 hour

the answer Part b) is
0.154 hour

Part c) Use your answers to a and b to determine how long, in hours, the full trip will take (1 mile uphill and 1 mile downhill). Give an exact answer expressed as a fraction in simplest terms and then give a decimal approximation correct to three decimal places

total time=0.182+0.154------> 0.336 hour
and
(2/11)+(2/13)----> (2*13+2*11)/(11*13)-----> (26+22)/(143)-----> 48/143 hour